Asymptotic entanglement in a two-dimensional quantum walk

The evolution operator of a discrete-time quantum walk involves a conditional shift in position space which entangles the coin and position degrees of freedom of the walker. After several steps, the coin-position entanglement (CPE) converges to a well defined value which depends on the initial state. In this work we provide an analytical method which allows for the exact calculation of the asymptotic reduced density operator and the corresponding CPE for a discrete-time quantum walk on a two-dimensional lattice. We use the von Neumann entropy of the reduced density operator as an entanglement measure. The method is applied to the case of a Hadamard walk for which the dependence of the resulting CPE on initial conditions is obtained. Initial states leading to maximum or minimum CPE are identified and the relation between the coin or position entanglement present in the initial state of the walker and the final level of CPE is discussed. The CPE obtained from separable initial states satisfies an additivity property in terms of CPE of the corresponding one-dimensional cases. Non-local initial conditions are also considered and we find that the extreme case of an initial uniform position distribution leads to the largest CPE variation.Comment: Major revision. Improved structure. Theoretical results are now separated from specific examples. Most figures have been replaced by new versions. The paper is now significantly reduced in size: 11 pages, 7 figure

Pain outcomes in patients with bone metastases from advanced cancer: assessment and management with bone-targeting agents

Bone metastases in advanced cancer frequently cause painful complications that impair patient physical activity and negatively affect quality of life. Pain is often underreported and poorly managed in these patients. The most commonly used pain assessment instruments are visual analogue scales, a single-item measure, and the Brief Pain Inventory Questionnaire-Short Form. The World Health Organization analgesic ladder and the Analgesic Quantification Algorithm are used to evaluate analgesic use. Bone-targeting agents, such as denosumab or bisphosphonates, prevent skeletal complications (i.e., radiation to bone, pathologic fractures, surgery to bone, and spinal cord compression) and can also improve pain outcomes in patients with metastatic bone disease. We have reviewed pain outcomes and analgesic use and reported pain data from an integrated analysis of randomized controlled studies of denosumab versus the bisphosphonate zoledronic acid (ZA) in patients with bone metastases from advanced solid tumors. Intravenous bisphosphonates improved pain outcomes in patients with bone metastases from solid tumors. Compared with ZA, denosumab further prevented pain worsening and delayed the need for treatment with strong opioids. In patients with no or mild pain at baseline, denosumab reduced the risk of increasing pain severity and delayed pain worsening along with the time to increased pain interference compared with ZA, suggesting that use of denosumab (with appropriate calcium and vitamin D supplementation) before patients develop bone pain may improve outcomes. These data also support the use of validated pain assessments to optimize treatment and reduce the burden of pain associated with metastatic bone disease

Counting independent sets in graphs with bounded bipartite pathwidth

The Glauber dynamics can efficiently sample independent sets almost uniformly at random in polynomial time for graphs in a certain class. The class is determined by boundedness of a new graph parameter called bipartite pathwidth. This result, which we prove for the more general hardcore distribution with fugacity λ, can be viewed as a strong generalisation of Jerrum and Sinclair’s work on approximately counting matchings. The class of graphs with bounded bipartite path-width includes line graphs and claw-free graphs, which generalise line graphs. We consider two further generalisations of claw-free graphs and prove that these classes have bounded bipartite pathwidth

Erythropoiesis-stimulating agents in oncology: a study-level meta-analysis of survival and other safety outcomes

BACKGROUND: Cancer patients often develop the potentially debilitating condition of anaemia. Numerous controlled studies indicate that erythropoiesis-stimulating agents (ESAs) can raise haemoglobin levels and reduce transfusion requirements in anaemic cancer patients receiving chemotherapy. To evaluate recent safety concerns regarding ESAs, we carried out a meta-analysis of controlled ESA oncology trials to examine whether ESA use affects survival, disease progression and risk of venous-thromboembolic events

Amplifying the Security of Functional Encryption, Unconditionally

Security amplification is a fundamental problem in cryptography. In this work, we study security amplification for functional encryption (FE). We show two main results: 1) For any constant epsilon in (0,1), we can amplify any FE scheme for P/poly which is epsilon-secure against all polynomial sized adversaries to a fully secure FE scheme for P/poly, unconditionally. 2) For any constant epsilon in (0,1), we can amplify any FE scheme for P/poly which is epsilon-secure against subexponential sized adversaries to a fully subexponentially secure FE scheme for P/poly, unconditionally. Furthermore, both of our amplification results preserve compactness of the underlying FE scheme. Previously, amplification results for FE were only known assuming subexponentially secure LWE. Along the way, we introduce a new form of homomorphic secret sharing called set homomorphic secret sharing that may be of independent interest. Additionally, we introduce a new technique, which allows one to argue security amplification of nested primitives, and prove a general theorem that can be used to analyze the security amplification of parallel repetitions